Publications and preprints

[this research is/was supported by the following grants

ANR-09-JCJC-0099-01  / 2009-2013

ANR-13-BS01-0007-01, ANR-13-JS01-0006 /   2013-2017

ERC Consolidator grant IPFLOW /    2017-2023 ]


Recent preprints

Conformal field theory and probability:

C. Guillarmou, R. Rhodes, B. Wu Conformal Bootstrap for surfaces with boundary in Liouville CFT. Part 1: Segal axioms ,
 Preprint [arXiv:2408.13133]

C. Guillarmou, T. Gunaratnam, V.Vargas, 2d Sinh-Gordon model on the infinite cylinder ,
 Preprint [arXiv:2405.04076]

C. Guillarmou, A. Kupiainen, R. Rhodes, Review on the probabilistic construction and conformal bootstrap in Liouville theory ,
 Preprint [arXiv:2403.12780]

G. Baverez, C. Guillarmou, A. Kupiainen, R. Rhodes, Semigroup of annuli in Liouville Theory ,
 Preprint [arXiv:2403.10914]

C. Guillarmou, A. Kupiainen, R. Rhodes, Compactified Imaginary Liouville Theory ,
 Preprint [arXiv:2310.18226]

G. Baverez, C. Guillarmou, A. Kupiainen, R. Rhodes, V. Vargas, The Virasoro structure and the scattering matrix for Liouville conformal field theory ,
 Probability and Math. Physics [arXiv:2204.02745]

C. Guillarmou, A. Kupiainen, R. Rhodes, V. Vargas, Segal axioms and bootstrap for Liouville Theory ,
 preprint [arXiv:2112.14859]

C. Guillarmou, A. Kupiainen, R. Rhodes, V. Vargas, Conformal bootstrap in Liouville Theory,
 Acta Mathematica, to appear. [arXiv:2005.11530].
The article by Quanta Magazine and the Video on our work

Rigidity and inverse problems:

C. Guillarmou, M. Mazzucchelli, An introduction to geometric inverse problems ,
 Book, preliminary version (comments welcome)

C. Guillarmou, T. Lefeuvre, G. Paternain, Marked length spectrum rigidity for Anosov surfaces ,
 Duke Math J, to appear. [arXiv:2303.12007]

M. Cekic, C. Guillarmou, T. Lefeuvre, Local lens rigidity for manifolds of Anosov type ,
 Analysis and PDE, to appear [arXiv:2204.02476]

Y. Guedes Bonthonneau, C. Guillarmou, T. Weich, SRB measures for Anosov actions,
 Journal of Differential Geometry [arXiv:2103.12127]

Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, T. Weich, Ruelle-Taylor resonances of Anosov actions
Journal of the EMS, to appear. [arXiv:2007.14275]


Published papers organized by theme :

Quantum resonances and scattering theory in hyperbolic geometry

C. Guillarmou, Resonances sur les varietes asymptotiquement hyperboliques.
2004. PhD thesis.

C. Guillarmou, Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds.
Duke Math. Journal  129 (2005), no. 1., 1-37. [Arxiv math.SP/0311424].

C. Guillarmou, Absence of resonance near the critical line on asymptotically hyperbolic manifolds.
Asymptotic Analysis 42 (2005), no. 1-2, 105-121. [Arxiv math.SP/0406496]. 

C. Guillarmou, Resonances and scattering poles on asymptotically hyperbolic manifolds.
Math. Research Letters 12 (2005), no. 1, 103-119. [Arxiv math.DG/0403545].

C. Guillarmou, Resonances on some geometrically finite hyperbolic manifolds.
Communications. in Partial Differential Equations 31 (2006), 445,467. [Arxiv math.SP/0412064].

C. Guillarmou, F. Naud, Wave 0-trace and length spectrum on convex co-compact hyperbolic manifolds, 
Communications in Analysis and Geometry 14 (2006), no 5, 945-967. [Arxiv math.DG/0606223]

C. Guillarmou, Scattering on geometrically finite hyperbolic quotients with rational cusps.
Cubo Journal (special issue for the Proceedings of the second symposium in Spectral Theory and Scattering) (2009), 33 pages.

C. Guillarmou, Generalized Krein formula, determinants and Selberg zeta function in even dimension.
American Journal of Math. 131 (2009), no 5. [Arxiv math.SP/0512173] .

C. Guillarmou, A. Sa Barreto, Scattering and inverse scattering on ACH manifolds,
J. Reine Angew. Math. 622 (2008), 1-55. [Arxiv math.AP/0605538]

C. Guillarmou, F. Naud, Wave decay on convex co-compact hyperbolic manifolds.
Comm. Math. Physics. 287, (2009), no 2, 489-511.[arXiv:0802.1345]

C. Guillarmou, S. Moroianu, J. Park, Eta invariant and Selberg zeta function of odd type over convex co-compact hyperbolic manifolds.
Advances in Math. 225 (2010), no 5, 2464-2516. [arXiv:0901.4082].

C. Guillarmou, R. Mazzeo, Resolvent of the Laplacian on geometrically finite hyperbolic manifolds
Inventiones Math 187 (2012) no 1, 99-144. [arXiv: 1002.2165].

S. Dyatlov, C. Guillarmou, Scattering phase asymptotics with fractal remainders,
Comm. Math. Phys. 324 (2013), no. 2, 425-444. [arXiv:1205.5955]

D. Borthwick, C. Guillarmou, Upper bounds on the number of resonances on geometrically finite hyberbolic manifolds.
Journal of EMS. 18 (2016), Issue 5, 997-1041. [arXiv 1303.7471]

Dirichlet-to-Neumann map and Calderon projector

C. Guillarmou, S. Moroianu, J. Park, Calderon and Bergman projectors on spin manifolds with boundary.
Journ. Geom. Anal. 24 (2014), no. 1, 298–336. [arXiv:1009.3179]

C. Guillarmou, L. Guillopé, The determinant of the Dirichlet-to-Neumann map for surfaces with boundary ,
Int. Math. Res. Not. (2007), no. 22, Art. ID rnm099. [Arxiv math.SP/0701727]

Poincare-Einstein manifolds and conformal geometry

E. Aubry, C. Guillarmou, Conformal harmonic forms, Branson-Gover operators and Dirichlet problem at infinity.
Journ. Eur. Math. Soc. 13 (2011), no 4, 911-957. [arXiv:0808.0552]

C. Guillarmou, J. Qing, Spectral characterization of Poincare-Einstein manifold with infinity of positive Yamabe type.
Int. Math. Res. Not. (2010), 1720-1740. [arXiv:0909.3207].

C. Guillarmou, S. Moroianu, J-M. Schlenker, The renormalized volume and uniformisation of conformal structures.
Journal Institut Math. Jussieu, DOI: https://doi.org/10.1017/S1474748016000244. [arXiv 1211.6705]

 Semiclassical Random walks

H. Christianson, C. Guillarmou, L. Michel, Random walk on surfaces with hyperbolic cusps,
Annales IHP 12 (2011), 743-775. [arXiv: 1005.2754]

C. Guillarmou, L. Michel, Spectral analysis of random walk operators on Euclidean space,
Math. Research Letters 18 (2011), no 3, 405-424. [arXiv: 1006.3065]

Teichmuller theory and hyperbolic 3-manifolds

C. Guillarmou, S. Moroianu, Chern-Simons line bundle on Teichmuller space,
Geometry and Topology, 18 (2014) 327–377. [arXiv: 1102.1981]

C. Guillarmou, S. Moroianu, F. Rochon, Renormalized volume on the Teichmuller space of puntured surfaces,
Ann. Scuola Normale Pisa, 5 (2017), Vol 17, 323-384.  [arXiv: 1504.04721]

Harmonic analysis

C. Guillarmou, A. Hassell, The resolvent at low energy and Riesz transform for Schrodinger operators on asymptotically conic manifolds, Part I.
Math Annalen. 341 (2008), no 4, 859-896. [Arxiv math.AP/0701515]

C. Guillarmou, A. Hassell, The resolvent at low energy and Riesz transform for Schrodinger operators on asymptotically conic manifolds, Part II
Ann. Inst. Fourier. 59 (2009), no 2, 1553-1610. [Arxiv math/0703316].

N. Burq, C. Guillarmou, A. Hassell, Strichartz estimates without loss on manifolds with hyperbolic trapped geodesics.
GAFA 20 (2010), 627-656. [arXiv: 0907.3545].

C. Guillarmou, A. Hassell, A. Sikora, Resolvent at low energy III: the spectral measure,
Transactions of the AMS 365 (2013), 6103-6148. [arXiv: 1009.3084]

C. Guillarmou, A. Hassell, A. Sikora, Restriction and spectral multiplier theorems on asymptotically conic manifolds.
Analysis and PDE 6 (2013), no 4, 893-950. [arXiv: 1012.3780]

C. Guillarmou, A. Hassell, Uniform Sobolev estimates for non-trapping metrics,
Journal of Inst. Math. Jussieu, Vol 13, Issue 3, (2014), 599-632. [arXiv: 1205.4150]

C. Guillarmou, D. Sher, Low energy resolvent for the Hodge Laplacian. Applications to Riesz transform, Sobolev estimates and analytic torsion,
IMRN, doi:10.1093/imrn/rnu119 . [arXiv: 1310.4694]

C. Guillarmou, A. Hassell, K. Krupchyk Eigenvalue bounds for non-self-adjoint Schrodinger operators with non-trapping metrics,
Analysis and PDE 13(2020), no 6, 1633-1670. DOI 10.2140/apde.2020.13.1633.[arXiv:1709.09759]


Inverse problems and rigidity questions

C. Guillarmou, A. Sa Barreto, Inverse Problems for Einstein manifolds.
Inverse Problems and Imaging. 3 (2009), no 1, 1-15. [arXiv:0710.1136].

C. Guillarmou, L. Tzou, Calderon inverse problem on Riemann surfaces.
Proceedings of CMA 44 (2009), 129-142. Volume for the AMSI/ANU workshop on Spectral Theory and Harmonic Analysis. [arXiv:0904.3804]

C. Guillarmou, L. Tzou, Calderon inverse problem with partial data on Riemann surfaces
Duke Math. J. 158 (2011), no 1, 83-120.  [arXiv:0908.1417].

C. Guillarmou, M. Salo, L. Tzou, Inverse scattering at fixed energy for surfaces with Euclidean ends.
Comm. Math. Phys. 303 (2011), no 3, 761-784 . [arXiv: 1004.0315].

C. Guillarmou, L. Tzou, Identification of a connection from Cauchy data space on a Riemann surface with boundary,
GAFA 21 (2011), no 2, 393-418. [arXiv: 1007.0360]

P. Albin, C. Guillarmou, L. Tzou, G. Uhlmann, Inverse boundary problems for systems in two dimensions,
Annales IHP, 14 (2013), no 6, 1551-1571. [arXiv:1105.4565]

C. Guillarmou, Invariant Distributions and X-ray transform for Anosov flows,
Journal of Differential Geometry, 105 (2017), 177-208. [arXiv: 1408.4732]

C. Guillarmou, G. Paternain, M. Salo, G. Uhlmann, The X-ray transform for connections in negative curvature,
Comm. Math. Phys.  343 (2016), no 1, pp 83-127. [arXiv: 1502.04720]

C. Guillarmou, Lens rigidity for manifolds with hyperbolic trapped set,
J. Amer. Math. Soc. 30 (2017), 561-599. [arXiv: 14102.1760]

C. Guillarmou, M. Mazzucchelli, Marked boundary rigidity for surfaces
Ergodic Theory and Dynamical Systems, DOI: https://doi.org/10.1017/etds.2016.94. [arXiv:1602.02946]

C. Guillarmou, F. Monard, Reconstruction formulas for X-ray transforms in negative curvature.
Annales Institut Fourier 67 (2017), no. 4, p. 1353-1392   [arXiv:1511.05516]

R. Graham, C. Guillarmou, P. Stefanov, G. Uhlmann, X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds.
Ann. Inst. Fourier, 69 (2019), no. 7, 2857-2919. Past, Present and Future an homage to Marcel Berger. [arXiv:1709.05053]

C. Guillarmou, M. Salo, L. Tzou, The linearized Calderon problem on complex manifolds
Acta Math Sinica, English Series, 35 (2019), no 6 1043-1056. Special volume in honour of Carlos Kenig. [arXiv:1805.00752]

C. Guillarmou, T. Lefeuvre, The marked length spectrum of Anosov manifolds
Annals of Math 190 (2019), no 1., 321-344. [arXiv:1806.04218]

C. Guillarmou, M. Mazzucchelli, L. Tzou, Boundary and lens rigidity for non-convex manifolds,
American J. Math. . 143 (2021), no 2, 533--575. [arXiv:1711.10059]

C. Guillarmou, G. Knieper, T. Lefeuvre, Geodesic stretch, pressure metric and marked length spectrum rigidity,
 Ergodic Theory and Dynamical Systems, special volume in memory of Anatole Katok, to appear. [arXiv:1909.08666]

C. Guillarmou, M. Lassas, L. Tzou, X-ray transform in asymptotically conic spaces,
 International Mathematics Research Notices, (2020), rnaa286. [arXiv:1910.09631]

C. Guillarmou, M. Mazzucchelli, L. Tzou, Asymptotically Euclidean metrics without conjugate points are flat,
 Journal of Geometric Analysis 33 (2023) no 37 (2023).[arXiv:1909.01488]

Y. Guedes Bonthonneau, C. Guillarmou, M. Jezequel, Scattering rigidity for analytic metrics ,
 Cambridge Journal of Math. 12 (2024), no 1, 165--222 [arXiv:2201.02100]

V. Arnaiz, C. Guillarmou, Stability estimates in inverse problems for the Schrodinger and wave equations with trapping ,
 Rev. Mat. Iberoam. 39 (2023), no. 2, pp. 495--538. [arXiv:2106.11167]

Hyperbolic dynamics and Ruelle resonances:


Semiclassical measures, quantum chaos

C. Guillarmou, F. Naud, Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds.
American Journal of Math, 136 (2014), no 2,  445-479. [arXiv:1107.2655]

S. Dyatlov, C. Guillarmou, Microlocal limits of plane waves and Eisenstein functions.
Annales de l'ENS,  (4) 47 (2014) no 2, 371-448. [arXiv:1204.1305]

Dynamical systems, Ruelle resonances

S. Dyatlov, F. Faure, C. Guillarmou, Power spectrum of the geodesic flow on hyperbolic manifolds,
Analysis and PDE 8 (2015), 923–1000.  [arXiv:1403.0256]

S. Dyatlov, C. Guillarmou, Pollicott-Ruelle resonances for open systems,
Annales IHP, 17 (2016), no 11, pp 3089–3146. [arXiv: 1410.5516]

C. Guillarmou, J. Hilgert, T. Weich, Classical and quantum resonances for hyperbolic surfaces.
Math. Annalen 370 (2018), Volume 370, Issue 3-4, pp 1231-1275. [arXiv:1605.08801]

S. Dyatlov, C. Guillarmou, Dynamical zeta functions for Axiom A flows
Bull. AMS, 55 (2018), 337--342. [arXiv:1801.00348]

F. Faure, C. Guillarmou, Horocyclic invariance of Ruelle resonant states for contact Anosov flows in dimension 3.
Math Research Letters, 25 (2018), no 5, 1405--1427.. [arXiv:1705.07965]

N.V. Dang, C. Guillarmou, G. Riviere, S. Shen, Fried Conjecture in small dimensions,
 Inventiones Math. 220 (2020), 525-579. [arXiv:1807.01189] 

C. Guillarmou, J. Hilgert, T. Weich, High frequency limits for invariant Ruelle densities
Annales Henri Lebesgue, Volume 4 (2021) , pp. 81-119. [arXiv:1803.06717]

C. Guillarmou, B. Kuster, Spectral theory of the frame flow on hyperbolic 3-manifolds (with an appendix by Charles Hadfield),
 Annales Henri Poincare 22 (2021), 3565--3617. [arXiv:2005.08387]

M. Cekic, C. Guillarmou, First band of Ruelle resonances for contact Anosov flows in dimension 3,
 Comm. Math. Phys. 386 (2021), 1289--1318 [arXiv:2011.05959]

C. Guillarmou, T. de Poyferré, with an Appendix by Y. Guedes Bonthonneau A paradifferential approach for hyperbolic dynamical systems and applications,
 Tunisian Journal of Math 4 (2022), No. 4, 673--718. [arXiv:2103.15397]

Quantum and Conformal Field Theory

C. Guillarmou, R. Rhodes, V. Vargas,  Polyakov's formulation of 2d bosonic string theory.
Publications mathematiques de l'IHES,130 (2019), 11-185. [arXiv:1607.08467]

Proceedings, Survey, and others:

Survey on Calderon inverse problem in dimension 2, (2011), joint with Leo Tzou,
Inside Out II, edited by Gunther Uhlmann, MSRI.

Semiclassical measures for generalized plane waves, (2012),
Séminaire X EDP.

Scattering for the geodesic flow on surfaces with boundary, (2015),
Mini course in Montreal.

Rigidités spectrales: un bref état de l'art, (2021),
Article for la Gazette des mathématiciens (SMF)

Books

Operateurs géometriques, invariants conformes et variétés asymptotiquement hyperboliques. Joint with Zindine Djadli and Marc Herzlich.
Panorama et Synthèse SMF, (2008).

An Introduction to Geometric Inverse Problems, joint with M. Mazzucchelli.